Vol. 292, No. 1, 2018

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ISSN: 0030-8730
Meridional rank and bridge number for a class of links

Michel Boileau, Yeonhee Jang and Richard Weidmann

Vol. 292 (2018), No. 1, 61–80
Abstract

We prove that links with meridional rank 3 whose 2-fold branched covers are graph manifolds are 3-bridge links. This gives a partial answer to a question by S. Cappell and J. Shaneson on the relation between the bridge numbers and meridional ranks of links. To prove this result, we also show that the meridional rank of any satellite knot is at least 4.

Keywords
knot, link, bridge number, meridian, meridional rank, 2-fold branched cover, graph manifold
Mathematical Subject Classification 2010
Primary: 57M25
Milestones
Received: 7 November 2015
Revised: 3 May 2017
Accepted: 22 May 2017
Published: 22 September 2017
Authors
Michel Boileau
Aix-Marseille Univ.
CNRS, Centrale Marseille
Marseille
France
Yeonhee Jang
Department of Mathematics
Nara Women’s University
Kitauoyanishi-machi
Nara
Japan
Richard Weidmann
Mathematisches Seminar
Christian-Albrechts-Universität zu Kiel
Kiel
Germany